You earn Style Points while playing the single player campaign which you can use to buy art, videos, and multiplayer characters from the Unlock Shop. You must purchase all of the Multiplayer characters to earn this achievement. That will take 5,350 Style Points.
First, play through the campaign on Casual and Hard Boiled difficulty to earn all of the difficulty achievements before paying attention to this one. That should net you a good chunk of the Style Points you will need.
Finally, mop up any remaining points by going to Chapter Select and loading Chapter 1 - Hong Kong Marketplace, The Tea House. Simply swing from any of the chandeliers and shoot all of the enemies. Kill the boss when he comes and then exit to the main menu. Rinse and repeat. This should get you up to 150 Style Points every time.
Please refer to the attached video for more information.